Answer:
x=2.5
Step-by-step explanation:
We have,
4x+2=12
\implies4x=10
Taking log both the sides we have,
log\,4x=log\,10
\implies log\,4 + log\,x=log\,10 \left\:\: [ \because log\,ab = log\, a + log\, b\right ]
\implies log\,x=log\,10 -log\,4
\implies log\,x={ log\,(\frac{10}{4}) \:\:\left [\because log\,a -log\,b= log\,\frac{a}{b} \right ]
\implies log\,x=log\,2.5
\implies \frac{log\,x}{log\,2.5}=1
\implies log_{(2.5)}\, x=1\:\:\left [ \because log_{b}\,a=\frac{log\,a}{log\,b} \right ]
\implies x=(2.5)^{1}\:\: [ \because log_{b}\,a=m \implies a=b^{m} ]
Hence, we have x=2.5
